REDUCTION OF BIAS AND MEAN SQUARE ERROR IN ESTIMATING AR(1) MODEL PARAMETER BASED ON QUENOUILLE–TYPE AND OPTIMUM OVERLAPPING SERIES SPLITTING ESTIMATORS
Keywords:
AR(1), Bias, Mean Square Error, OLSE, Overlapping series(OS), Quenouille’s estimator.Abstract
The autocorrelation parameter of AR(1) model is estimated very often by the
ordinary least squares estimator (OLSE) due to its simplicity. The present in-
vestigation aims at deriving the algebraic expression of the covariance between
two OLSE’s obtainable from two overlapping (OS) or non-overlapping (NOS) or
gapping (GS) series whatsoever choosing from the given whole series. Such ex-
pression is used to obtain the expressions of bias, mean square error and variance
of Quenouille’s estimator (1956). Based on OS splitting, a Quenouille-type fam-
ily and another competent family of estimators are suggested. Their comparative
performances are discussed in respect of bias and mean square error.
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